and the version of Chromium which Electron 1.4.13 is using is merely 53.0.2785.143

So my question is “Is it possible to manually update the Chromium version” (I’m guessing it’s not possible as that lies in the foundations of Electron but still asking is still worthwhile) and if not any suggestions for FLAC playback?

Not really, It’s possible, but not practical as it requires a lot of work. Work to upgrade to Chromium 54 has been underway for weeks (this one is trickier than usual due to build system changes). Electron only uses stable Chromium releases, the latest stable release at the time of writing is Chromium 55, so you may need to wait a while for Chromium 56 to be available in Electron.